Kibbutz Kfar Azza, Israel — Their homes separated by a wheat field, barbed wire, and Israel's blockade of the Gaza Strip, it's been more than two years since Amir Efrat last saw the Gazan who helped him maintain the water systems in this collective.

But he has talked to him by phone – and could hear the despair that lurked behind the small talk. And so, about a month ago, he instructed the kibbutz treasurer to wire 500 shekels ($135) to an account in Gaza to help his unemployed friend support a family of nine children.

His friend never requested help, but "I felt him ask," says the rumpled kibbutznik. "There's no work. It's difficult."

The impoverished Strip has grown ever more isolated since Hamas took charge last June. But that hasn't choked off personal ties between Israelis and Gazans who once worked together daily. Talking regularly by phone, they update each other about families and friends – and about the toll of the ongoing hostilities. Transcending the politics that divide them, they reach out as best they can as individuals – the Gazans inquiring whether anyone has been hurt by the Qassam missiles fired by Palestinian militants and the Israelis asking about their troop movements inside Gaza.

Though the Israelis avoid politics, the cross-border friendships leave them conflicted about bringing relentless pressure to bear on Gaza's population of 1.5 million to stop the rockets that are fired toward cities and towns around Gaza. While only six rockets have landed on the kibbutz, hundreds have hit Sderot, just a five-minute drive to the north.

"The power outages are just, but it still breaks your heart," says Mr. Efrat, who points out the kibbutz's children's house, reinforced against the rockets that have fallen on Kfar Azza. "I don't think [Gazans] need to suffer so much. It definitely plays into the hands of Hamas."

Egyptian police moved Thursday to control the tens of thousands of Palestinians who streamed into the border town of Rafah a day earlier after militants blew up a border fence.

Meanwhile, Israel's Deputy Defense Minister said that with the Gaza-Egypt border breached, supplies of water, electricity, and food should come from Cairo.

For years before the outbreak of the Palestinian uprising in 2000, Israel and the Gaza Strip were joined at the hip. Hundreds of thousands of Gazans worked inside Israel by day and brought home salaries that were the mainstay of the coastal strip's economy. Kibbutz Kfar Azza – whose name is Hebrew for Gaza Village – used to employ more than a dozen Palestinians from Gaza.

But gradually, the economic links have been reduced. After Israel dismantled settlements and army bases in Gaza, it stopped giving entry permits, save for Gazans in need of medical treatment. When Hamas took control of Gaza, Israel reduced the operations of commercial crossings, allowing in only humanitarian aid.

"Now they're living off of flour and olives," says Dudi Doron, a Kfar Azza resident who keeps in regular contact with Mohammed, a laborer from the Gaza city of Khan Younis who worked on the kibbutz for 20 years but now is unemployed.

Though Mohammed calls from an Israeli cellphone given to him by Mr. Doron, the Khan Younis resident is hard to reach because of patchy networks.

About three months ago, Doron wired 4,000 shekels ($1,080) to a Gaza bank to help Mohammed's family make ends meet. But Doron still supports Israel's policy of stopping fuel supplies.

"Better to pressure this way than with tanks," he says, referring to comments by Israeli officials warning of a broad offensive in Gaza. "I prefer this to sending soldiers in there.... [W]e'll lose 200 people and they'll lose thousands."

Efrat, though, criticizes the expectation of some Israelis that pressure will prompt Gazans to turn on Hamas. "They know if they speak out, they'll get shot," he says.

The thuds of Palestinian Qassam rockets can be heard from Moshav Tekuma, an agricultural cooperative just east of Kfar Azza. In an office lined with Koranic and Talmudic texts, Avner Cohen, the retired religious affairs commissioner in Israel's civil administration for Gaza, often receives calls from former Palestinian staff and Islamic dignitaries.

"Avner sympathizes with me because he has children. He asks me, 'What do you need? What do you want?' I tell him I only want peace. I only want to coexist," says Fawaz el-Beitar, who worked as Mr. Cohen's driver and resides in Gaza City. "The last time I called him, I told him about the siege, I told him about the closure, I told him about our difficult life."

Back at the edge of Kibbutz Kfar Azza, Efrat peers westward toward a panoramic Gaza horizon that offers a map of the recent political tension.

In the distance to the north were the orchards of Beit Hanoun, used by militants to lob explosives into Israel. Closer to the kibbutz, to the south, is the empty cargo terminal of the Karni Crossing, the Gaza Strip's economic lifeline to the world. Straight ahead, at the outskirts of Gaza City, a line of trees and houses marks the village of his former colleague.

"There's his house," he gestures. But this week, Efrat got a call from the friend, who said he had moved in with his mother-in-law in Gaza City to get away from the fighting. "He doesn't have any interest in this war," he says. "Of course I'm worried."